In this paper we examine the theoretical limits on
developing algorithms to find blocking probabilities in a general loss
network. We demonstrate that exactly computing the blocking
probabilities of a loss network is a #P-complete problem. We also
show that a general algorithm for approximating the blocking
probabilities is also intractable unless RP=NP, which seems unlikely
according to current common notions in complexity theory. Given these
results, we examine implications for designing practical algorithms
for finding blocking probabilities in special cases.

Originally appeared in the Proceedings of the 6th Annual ACM
Symposium on Parallel Algorithms and Architectures,
pp. 346--353, 1994. Journal version invited to appear
in the special conference issue of Journal of Computer and
System Sciences, vol 53:3, pp. 317-327, December 1996.
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